Tamiyo’s first ability tracks the permanent, but not its controller. If the permanent changes controllers before its first controller’s next untap step has come around, then it won’t untap during its new controller’s next untap step.

5/1/2012

The number of tapped creatures the player controls is determined when Tamiyo’s second ability resolves.

5/1/2012

Tamiyo’s third ability creates one emblem with two abilities.

5/1/2012

If you activate Tamiyo’s third ability when she has eight loyalty counters on her, she’ll be put into your graveyard before the emblem is created. She won’t return to your hand.

5/1/2012

Cards that are put into your graveyard can be returned to your hand by the emblem’s ability even if they were never in your hand.

7/1/2013

The ability can target a tapped permanent. If the targeted permanent is already tapped when it resolves, that permanent just remains tapped and doesn’t untap during its controller’s next untap step.